Question

2.01: swbat explore and define special angle relationships created when 2 parallel lines are cut by a transversal
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**#1.) fill in the blanks with either \parallel lines\ or \transversal line\:
to determine whether we have alternate side or same side angles we look at the _, and to determine whether our angles are interior or exterior angles we look at the _
#2.) in the diagram below, a || b.
a. annotate the parallel lines, then fill in the chart below:

angles	angle pair name	relationship
∠1 and ∠3
∠4 and ∠6
∠8 and ∠2
∠1 and ∠4
∠2 and ∠7
∠3 and ∠7

b. **if m∠4 = 95°, fill in all angles in the diagram.

Explanation:

Step1: Analyze angle - side relationship

To determine if angles are alternate - side or same - side, we consider the parallel lines. Parallel lines help in identifying the position of angles relative to each other in terms of sides.

Step2: Analyze interior - exterior relationship

To determine if angles are interior or exterior, we look at the transversal line. The transversal divides the space around the parallel lines into interior and exterior regions.

Step3: Identify angle - pair names and relationships for #2a

• $\angle1$ and $\angle3$: Vertical angles, equal in measure.
• $\angle4$ and $\angle6$: Alternate interior angles, equal in measure since $a\parallel b$.
• $\angle8$ and $\angle2$: Corresponding angles, equal in measure since $a\parallel b$.
• $\angle1$ and $\angle4$: Linear pair, supplementary ($\angle1+\angle4 = 180^{\circ}$).
• $\angle2$ and $\angle7$: Alternate exterior angles, equal in measure since $a\parallel b$.
• $\angle3$ and $\angle7$: Corresponding angles, equal in measure since $a\parallel b$.

Step4: Find angle measures for #2b

If $m\angle4=95^{\circ}$:

• $\angle1$ and $\angle4$ are a linear pair, so $m\angle1 = 180 - 95=85^{\circ}$.
• $\angle1$ and $\angle3$ are vertical angles, so $m\angle3 = 85^{\circ}$.
• $\angle2$ and $\angle4$ are vertical angles, so $m\angle2 = 95^{\circ}$.
• $\angle4$ and $\angle6$ are alternate - interior angles, so $m\angle6 = 95^{\circ}$.
• $\angle6$ and $\angle8$ are vertical angles, so $m\angle8 = 95^{\circ}$.
• $\angle5$ and $\angle7$ are vertical angles, and $\angle5$ and $\angle4$ are corresponding angles, so $m\angle5 = 95^{\circ}$ and $m\angle7 = 95^{\circ}$.

Answer:

#1: parallel lines; transversal line
#2a:

Angles	Angle Pair Name	Relationship
$\angle4$ and $\angle6$	Alternate interior angles	Equal
$\angle8$ and $\angle2$	Corresponding angles	Equal
$\angle1$ and $\angle4$	Linear pair	Supplementary
$\angle2$ and $\angle7$	Alternate exterior angles	Equal
$\angle3$ and $\angle7$	Corresponding angles	Equal

#2b: $m\angle1 = 85^{\circ}$, $m\angle2 = 95^{\circ}$, $m\angle3 = 85^{\circ}$, $m\angle5 = 95^{\circ}$, $m\angle6 = 95^{\circ}$, $m\angle7 = 95^{\circ}$, $m\angle8 = 95^{\circ}$